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Subgroup label Subgroup order Cyclic Abelian Solvable
Normal Characteristic Perfect Maximal Central
Ambient label Ambient order Direct product Semidirect product
Quotient label Subgroup index Cyclic quotient Abelian quotient Solvable quotient
Maximal quotient Non-trivial proper Hall subgroup Sylow subgroup
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Results (43 matches)

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Label Subgroup Ambient Quotient
Name Order Sylow norm char max cent ab Name Order Name Size max ab
169869312.nb.1.a1.a1 $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_1$ $1$ ✓
169869312.nb.2._.A $C_2\times C_2^{10}.A_4^3:S_4$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.nb.2._.B $C_2^{10}.(C_4\times A_4^3:A_4)$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.nb.2._.C $C_2\times C_2^{10}.A_4^3:S_4$ $2^{20} \cdot 3^{4}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2$ $2$ ✓
169869312.nb.4._.A $C_2\times C_2^{10}.A_4^3:A_4$ $2^{19} \cdot 3^{4}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^2$ $2^{2}$ ✓
169869312.nb.6._.A $C_2^{12}.C_6^3.C_2^5$ $2^{20} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $S_3$ $2 \cdot 3$
169869312.nb.8._.A $C_2^{10}.A_4^3:A_4$ $2^{18} \cdot 3^{4}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $D_4$ $2^{3}$
169869312.nb.12._.A $C_2^{12}.C_6^3.C_2^4$ $2^{19} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $D_6$ $2^{2} \cdot 3$
169869312.nb.24._.A $C_2^{12}.C_3^3.C_2^6$ $2^{18} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $D_{12}$ $2^{3} \cdot 3$
169869312.nb.24._.B $C_2^{12}.C_6^3.C_2^3$ $2^{18} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
169869312.nb.24._.C $C_2^{12}.C_6^3.C_2^3$ $2^{18} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
169869312.nb.24._.D $C_2^{12}.C_6^3.C_2^3$ $2^{18} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $S_4$ $2^{3} \cdot 3$
169869312.nb.48._.A $C_2^{12}.C_6^3.C_2^2$ $2^{17} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2\times S_4$ $2^{4} \cdot 3$
169869312.nb.48._.B $C_2^{12}.C_6^3.C_2^2$ $2^{17} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2\times S_4$ $2^{4} \cdot 3$
169869312.nb.48._.C $C_2^{12}.C_6^3.C_2^2$ $2^{17} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2\times S_4$ $2^{4} \cdot 3$
169869312.nb.96._.A $C_2^{12}.C_6^3.C_2$ $2^{16} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^2:S_4$ $2^{5} \cdot 3$
169869312.nb.96._.B $C_2^{12}.C_3.D_6^2$ $2^{16} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_4:S_4$ $2^{5} \cdot 3$
169869312.nb.96._.C $C_2^{12}.C_6^3.C_2$ $2^{16} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_4:S_4$ $2^{5} \cdot 3$
169869312.nb.96._.D $C_2^{12}.C_3.D_6^2$ $2^{16} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_4:S_4$ $2^{5} \cdot 3$
169869312.nb.192._.C $C_2^{12}.C_6^3$ $2^{15} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^3:S_4$ $2^{6} \cdot 3$
169869312.nb.384._.A $C_2^{12}.C_3.C_6^2$ $2^{14} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^4:D_{12}$ $2^{7} \cdot 3$
169869312.nb.648._.A $C_2^{15}.C_2^3$ $2^{18}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_3^3:S_4$ $2^{3} \cdot 3^{4}$
169869312.nb.768._.A $C_2^{12}.C_3^3.C_2$ $2^{13} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^5:S_4$ $2^{8} \cdot 3$
169869312.nb.1296._.A $C_2^{15}.C_2^2$ $2^{17}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2\times C_3^3:S_4$ $2^{4} \cdot 3^{4}$
169869312.nb.1536._.A $C_2^{12}.C_3^3$ $2^{12} \cdot 3^{3}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^6:D_{12}$ $2^{9} \cdot 3$
169869312.nb.2592._.A $C_2^{14}.C_2^2$ $2^{16}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $(C_3^2\times C_{12}):S_4$ $2^{5} \cdot 3^{4}$
169869312.nb.2592._.B $C_2^{15}.C_2$ $2^{16}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $(C_3\times C_6^2):S_4$ $2^{5} \cdot 3^{4}$
169869312.nb.5184._.A $C_2^{15}$ $2^{15}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_6^3:S_4$ $2^{6} \cdot 3^{4}$
169869312.nb.10368._.A $C_2^{14}$ $2^{14}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $(C_6^2\times C_{12}):S_4$ $2^{7} \cdot 3^{4}$
169869312.nb.20736._.A $C_2^{13}$ $2^{13}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_6:D_6^2:S_4$ $2^{8} \cdot 3^{4}$
169869312.nb.41472._.A $C_2^9.C_2^3$ $2^{12}$ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4^3:S_4$ $2^{9} \cdot 3^{4}$
169869312.nb.41472._.B $C_2^{12}$ $2^{12}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_{12}:D_6^2.S_4$ $2^{9} \cdot 3^{4}$
169869312.nb.82944._.A $C_2^{11}$ $2^{11}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2\times A_4^3:S_4$ $2^{10} \cdot 3^{4}$
169869312.nb.165888._.A $C_2^{10}$ $2^{10}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4^3.C_4:S_4$ $2^{11} \cdot 3^{4}$
169869312.nb.165888._.B $C_2^8\times C_4$ $2^{10}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4:S_4^2.S_4$ $2^{11} \cdot 3^{4}$
169869312.nb.331776._.A $C_2^9$ $2^{9}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4^3.C_2^3:S_4$ $2^{12} \cdot 3^{4}$
169869312.nb.663552._.A $C_2^8$ $2^{8}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4^3.C_2^4:D_{12}$ $2^{13} \cdot 3^{4}$
169869312.nb.1327104._.A $C_2^7$ $2^{7}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4^3.C_2^5:S_4$ $2^{14} \cdot 3^{4}$
169869312.nb.2654208._.A $C_2^6$ $2^{6}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $A_4^3.C_2^6:D_{12}$ $2^{15} \cdot 3^{4}$ ✓
169869312.nb.21233664._.A $C_2^3$ $2^{3}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^9.A_4^3:S_4$ $2^{18} \cdot 3^{4}$
169869312.nb.42467328._.A $C_2^2$ $2^{2}$ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^{12}.C_3^3.C_2^4.D_{12}$ $2^{19} \cdot 3^{4}$ ✓
169869312.nb.84934656._.A $C_2$ $2$ ✓ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^{12}.C_3^3.C_2^6.D_6$ $2^{20} \cdot 3^{4}$ ✓
169869312.nb.169869312.a1.a1 $C_1$ $1$ ✓ ✓ ✓ ✓ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$ $C_2^{10}.A_4^3:A_4.D_4$ $2^{21} \cdot 3^{4}$
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